Abstract
For cycles of length 8 in a Tanner graph, we propose an identification procedure based on the analysis of paths in a protograph. We formulate and prove a number of theorems that introduce identification rules for cycles and restrict the number of subgraphs to be analyzed. To distinguish between them, we propose a number of parameters that uniquely determine the group of analyzed paths in the protograph.
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Tanner, R.M., On Quasi-cyclic Repeat-Accumulate Codes, in Proc. 37th Allerton Conf. on Communication, Control and Computing, Monticello, IL, USA, Sept. 22–24, 1999, pp. 249–259.
Fossorier, M.P.C., Quasi-cyclic Low-Density Parity-Check Codes from Circulant Permutation Matrices, IEEE Trans. Inform. Theory, 2004, vol. 50, no. 8, pp. 1788–1793.
Fan, J.L., Array Codes as Low-Density Parity-Check Codes, in Proc. 2nd Int. Symp. on Turbo Codes and Related Topics, Brest, France, Sept. 4–7, 2000, pp. 543–546.
Richardson, T.J., Shokrollahi, M.A., and Urbanke, R.L., Design of Capacity-Approaching Irregular Low-Density Parity-Check Codes, IEEE Trans. Inform. Theory, 2001, vol. 47, no. 2, pp. 619–637.
Li, Z., Chen, L., Zeng, L., Lin, S., and Fong, W.H., Efficient Encoding of Quasi-cyclic Low-Density Parity-Check Codes, IEEE Trans. Commun., 2006, vol. 54, no. 1, pp. 71–81.
Kschischang, F.R., Frey, B.J., and Loeliger, H.-A., Factor Graphs and the Sum-Product Algorithm, IEEE Trans. Inform. Theory, 2001, vol. 47, no. 2, pp. 498–519.
Tian, T., Jones, C.R., Villasenor, J.D., and Wesel, R.D., Selective Avoidance of Cycles in Irregular LDPC Code Construction, IEEE Trans. Commun., 2004, vol. 52, no. 8, pp. 1242–1247.
Mao, Y. and Banihashemi, A.H., A Heuristic Search for Good Low-Density Parity-Check Codes at Short Block Lengths, in Proc. 2001 IEEE Int. Conf. on Communications (ICC’2001), Helsinki, Finland, June 11–14, 2001, vol. 1, pp. 41–44.
Karimi, M. and Banihashemi, A.H., On the Girth of Quasi Cyclic Protograph LDPC Codes, IEEE Trans. Inform. Theory, 2013, vol. 59, no. 7, pp. 4542–4552.
Diouf, M., Declercq, D., Fossorier, M., Quya, S., and Vasić, B., Improved PEG Construction of Large Girth QC-LDPC Codes, in Proc. 9th Int. Symp. on Turbo Codes & Iterative Information Processing (ISTC’2016), Brest, France, Sept. 5–9, 2016, pp. 146–150.
Hu, X.-Y., Eleftheriou, E., and Arnold, D.M., Regular and Irregular Progressive Edge-Growth Tanner Graphs, IEEE Trans. Inform. Theory, 2003, vol. 51, no. 1, pp. 386–398.
Ovinnikov, A.A., Images of Cycles of Cyclic Liftings in the Base Graph of Protograph LDPC Codes, Tsifrovaya Obrabotka Signalov, 2016, no. 4, pp. 26–30.
Acknowledgements
The authors are especially grateful to A.N. Voropaev for his assistance in proving Theorem 2 and to a reviewer for careful reading of the manuscript and valuable remarks, which helped them to improve the final presentation.
Funding
The research was carried out at the expense of the Russian Science Foundation, project no. 17-79-20302.
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Russian Text © The Author(s), 2020, published in Problemy Peredachi Informatsii, 2020, Vol. 56, No. 2, pp. 82–94.
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Kharin, A.V., Zavertkin, K.N. & Ovinnikov, A.A. Detecting Cycles of Length 8 in the Tanner Graph of a QC-LDPC Code Based on Protograph Analysis. Probl Inf Transm 56, 173–184 (2020). https://doi.org/10.1134/S0032946020020039
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DOI: https://doi.org/10.1134/S0032946020020039